People often use that one event as the most important event of modern history, but how true is it? Obviously he was a very important guy, and that did kick off the events of the war, but what was the chance it would have happened anyway? They say Europe was a powder keg after all. Are there any other events that had a decent chance of happening that could have set the gears in motion?
Well before the war there were the the moroccan crisis. The first moroccan crisis happened due to the kaiser's declaration supporting the sovereignty of the sultan. The sultan proposed a conference to which France thought it wasn't necessary, yet Germany didn't thought it that way. Near to the brink of war, the main european powers decided to settle the affair at the Algeciras Conference. Years later, when the sultan faced a rebellion, the french were preparing to send troops arguing that it would protect european lives while the germans did the same by sending the Panther to Agadir. While the war seemed inevitable, the kaiser's backdown led to the french establish a protectorate over Morocco. The european powers were on the brink of war even before the archduke's assassination. Even if he was not killed, maybe colonial disputes, or another war in the balkans would have led to the war.
It was going to happen as tensions between the Great Powers were running high since the later part of the 19th Century.
France wanted revenge against Germany after the France-Prussian War (1870-1871) as Germany took away Alsace-Lorraine from France when they signed the Treaty of Frankfurt. This was further exacerbated that Bismarck (Germany's Chancellor at that time) further isolated France from any other potential allies by forming an alliance with Russia and Austria-Hungary.
The Congress of Berlin of 1878 caused major tensions to arise among Russia, Germany, Austria-Hungary and Britain. The Congress sought to revise the spoils of war that Russia obtained from the Treaty of San Stefano from the Russo-Turkish War that gave Russia too much influence in the Balkans through the creation of the Principality of Bulgaria. The Berlin Congress angered Russia as Bulgaria was reduced substantially in size, Britain took Cyprus and Austria-Hungary was allowed to administer but not annex Bosnia & Herzegovina. Russia was furious that it had finally fought a decisive war against the Ottomans and received so little while others benefited from Russia's actions. The Bosnian issue was to have further consequences on relations between the Great Powers in the 20th Century.
Tensions in the Balkans never subsided after that, with Pan-Slavism sweeping through the region and caused rebellions against the Ottomans to pop up, resulting in the formation of 3 new nations; Romania (1881), Serbia (1882) and Montenegro (1910). This nationalism was especially worrying for Austria as it caused its Southern provinces to be unstable and potentially exploding into uprisings as well. For Russia, it was welcoming as it portrayed itself as Protector of the Slavic Race, with these new nations further expanding Russia's influence in the region.
In 1908, Austria-Hungary undertook the annexation of Bosnia & Herzegovina, with the support of Russia in exchange for Austria-Hungary promoting Russia's cause for control of the Bosporus. Ultimately, Austria-Hungary reneged on the deal, leading to Russia losing face as it seemed as though the sold out the Slavic race.
The Balkan Wars also exploded tensions further, which was also a cause for the assassination. The wars made Serbia double in size, threatening Austria as there was a growing and violent Slavic nation in its backyard. Furthermore, the pro-Austrian monarch was also murdered by anti-Austrian men in a coup, making Austria even more suspicious of Serbia. The fact that the end of the Second Balkan Wars almost gave Serbia access to the sea (only denied by creation of Albania) made it clear that sooner or later, another Balkan Crisis would lead to an epic clash between Austria with Serbia and Russia (Serbia's ally).
The First and Second Moroccan Crisis enflamed tensions between Germany, France and Britain. As the other comment has already explained it, I won't get into more detail about it. But basically the crisis and Germany's foreign policy threatened Britain and France as Britain saw it as Germany trying to challenge the Royal Navy's control of the sea (essential to protect Britain's trade and empire). These events also pushed Britain to France's camp, making it seemed as though Germany was surrounded by a ring of enemies, with Russia in the East and France and Britain in the West.
The bottom line is that all these events could have caused a war but didn't. The resolution of each of these events only served to pent up more anger between nations due backing down. In the end, the assassination could have not caused war as well as Austria wasn't going to go to war without Germany's help and there was deliberation for a month before war was declared. However, that would have mean that war would have been declared over another event as well, dragging in all the Great Powers due to the web of alliances that bounded empires together.